A ship travels 50km on a bearing of 27 degrees, then travels on a bearing of 117 degrees for 140 km. Find the distance traveled from the starting point to the ending point.

This is simpler than it could be. Since the bearings differ by exactly 90 degrees, you have the legs of a right triangle. The distance d (in kilometers) traveled by the ship is given by the Pythagorean Theorem: .

The correct answer is approximately 148.66. In general, you need to know the turning angle for these types of problems. You would be using the law of cosines: , where C is the turning angle. In this case it was simpler because the turning angle is 90 degrees.